which would memoize those pesky exponentiations? (!! lets you retrieve elements from lists sort of as if they were arrays, with "subscripts" starting at zero.)

It was easy enough to try out, but the results were disappointing. Even on my Eee 900A, with a 32-bit processor that you'd think would get the most benefit, the variations in time output from one run to the next were large enough that I can't say with certainty that it made any difference at all. Time output for the first large data set:

real 0m1.093suser 0m1.068ssys 0m0.016s

For the second large data set:

real 0m5.531suser 0m5.472ssys 0m0.044s

These are with the program compiled--I still haven't done the file opening code.

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Therefore, I will follow the excellent advice of Stephen Diehl, and will not write a monad-analogy tutorial. Instead, I will say: do the 20 Intermediate Exercises, and take the Monad Challenges. To paraphrase Euclid, there is no royal road to Monads; the exercises and challenges take you down that road at whose end you'll see at least part of why Monads are so useful.

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foo = flip $ (flip mumble) . (flip frotz)

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